### Chapter 9, first assignment

Answers to selected problems for Chapter 9 are found here.

 Exercise 1. We do not feel the gravitational forces between ourselves and the objects around us because these forces are extremely small. Electrical forces, in comparison, are huge. Since we and the objects around us are composed of charged particles, why don't we usually feel electrical forces? The charged particles of which we are composed are balanced: each positive charge is balanced by a negative charge, so that overall we are electrically neutral. Any imbalance in electrical charge is quickly rectified by picking up charge from something else; that's the reason that we get little shocks in dry weather or in the winter. See the next exercise. Exercise 3. When combing your hair, you scuff electrons from your hair onto the comb. Is your hair then positively or negatively charged? How about the comb? The hair loses (negatively-charged) electrons; the comb gains them. Therefore your hair becomes positively charged and the comb becomes negatively charged. Exercise 4. An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin leaves of metal foil protected from air disturbances in a jar, as shown. When the ball is touched by a charged body, the leaves that normally hang straight down spread apart. Why? The leaves pick up like charges (positive or negative), and like charges repel! Exercise 9. The five thousand billion billion freely moving electrons in a penny repel one another. Why don't they fly out of the penny? The electrons' negative charges are balanced by the positively-charged atomic nuclei in the penny. The attractions between the positive and negative charges keep the electrons in the penny. Exercise 10. Two equal charges exert equal forces on each other. What if one charge has twice the magnitude of the other? How do the forces they exert on each other compare? Coulomb's law says that the electrical force between two charges is proportional to the product of their magnitudes: F ∝ q1q2. If we double q1, the electrical force will also double. Exercise 15. If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare? How will their accelerations compare? Their directions of travel? The forces acting on the electron and proton will have the same magnitude, because their charges have the same magnitude.The acceleration of the electron will be about 1800 times the acceleration of the proton, because a = F/m and the mass of the proton is about 1800 times that of the electron.The directions of travel will be 180° opposed, because the direction of force of the field on the proton will be opposite that of the electron (positive vs negative charges). Problem 4. A droplet of ink in an industrial ink-jet printer carries a charge of 1.6×10-10 C and is deflected onto paper by a force of 3.2×10-4 N. Find the strength of the electric field that is required to produce this force. The strength of the electric field is found by solving the Coulomb's Law expression that includes the information we know. Coulomb's Law is F = kq1q2/d2, where F is the force, k is the Coulomb's-Law constant (9×109 N m2/C2), q is the charge of the objects involved and d is a distance. The strength of an electric field is stated in coulombs per square meter. Letting S be field strength, 3.2×10-4 N = 9×109 N m2/C2 × 1.6×10-10 C × S 3.2×10-4 N ÷ (9×109 N m2/C2 × 1.6×10-10 C) = S S = 2.22×10-4 C/m2